The bitrate-efficient format (see the question's most voted answers and their comments thereunder) would be one that assures a good audio quality at a relatively lower bitrate.

In some cases one may need having files in mp3 format.

It seems that converting a lossy audio (like aac) to other lossy format with a "less efficient" bitrate, like mp3, imposes to use a somewhat higher bitrate for the output file in order to compensate its bitrate "inefficiency".

I understand that aac is amongst the most "efficient" - but what about others?

This logic can be applied to other lossy formats. I would like to know what lossy formats can be considered more (or less) efficient - in this sense - than the others.

This is really both content and encoder specific. If you had a file containing pure white noise, you would find that MP3/AAC might actually perform the worst (as they would drastically manipulate the frequency content of the resulting file). And that's when you have to start weighing the pros/cons of either assigning more bits, changing the encoder (or the parameters it uses), or even the codec you chose to begin with.
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BreakthroughMay 26 '13 at 16:58

In the future we might see Opus getting more exposure as well—it is specifically targeted at low bitrates.

In general, you can say that the AAC family of codecs is much more efficient than MP3. It is probably the codec of choice for most of today's applications.

There are various versions of AAC, depending on what features are used. Those are called "profiles". Particularly well known are AAC-LC (low complexity) and HE-AAC (high efficiency). The European Broadcasting Union (EBU) has published a detailed technical review of HE-AAC v2 in 2006, which gives more details about the implementation, its differences from "normal" AAC-LC and compares it to other codecs.

Also, MP3 is quite easily outperformed by AAC and Vorbis in low-bitrate scenarios.

Often, a codec specification only tells you how to decode (i.e. how to structure and parse the bitstream). This means there are no limits on how to write an encoder. Because of that, you can experience drastic differences in the subjective quality between two different MP3 encoders, for example. The same goes for AAC and Vorbis as well.

Since encoders are not standardized, there's quite a bit of competition on the market, and in some cases, "market leaders" have emerged, such as LAME in the section of free MP3 encoders, or FAAC for free AAC encoders (although fdk-aac is supposed to be better). Of course, commercial encoders such as the Fraunhofer MP3 encoder or the Nero AAC encoder exist as well.

It ultimately comes down to personal preference. Naturally, you can't objectively evaluate how "good" an encoder is. You need to get a number of people and have them listen to sound examples. This is called a codec listening test. There are multiple variants of tests, depending on what exactly you want to find out, e.g.:

Is codec A better than B? (For example, if AAC is better than MP3 at low bitrates)

Which codec is the best? (For example, all kinds of codecs are sorted by preference)

The possible combinations are near endless, and of course these tests are carried out with specific encoders (e.g. FAAC) rather than just testing "AAC" as a codec. As those tests take time and careful preparation, and the results cannot be summarized in one sentence, I suggest you take a look at Wikipedia's result section, where quite a number of test results have been publicized.

Depending on your application, you will find the "most efficient" format under the winners there. For example, here's a listening test taken from the EBU tech report I linked to above, which shows how AAC generally outperforms MP3 and Windows Media Audio at 48 kBit/s (low bitrate):

Thanks for the info. It's all mentioned in the EBU tech report though – I added a little more on that part but don't want to get all too technical.
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slhck♦May 15 '13 at 11:49

great answer. my intention was to know in relation to transcoding between lossy formats (that is mainly: from other lossy formats to mp3, beside aac>mp3 conversion, clarified in the answer i got to my other question) in which cases the bitrate of an output/less-efficient file should be increased. (that's why i ask which is more efficient.the idea is based on this answer). that is: should it be so for ogg>mp3? what about wma>mp3. i prefer to use flac when i can but mp3 is needed for some devices
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cipricusMay 15 '13 at 12:30

3

@cipricus For OGG → MP3 conversion you won't need to increase the bitrate as much as for WMA → MP3, but rather than aiming at specific numbers I suggest you take a few files that are representative of what you encode, and then listen to various bitrates. If you can't tell the difference anymore between the original and the transcode, stop increasing the bitrate.
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slhck♦May 15 '13 at 12:36